John Hench (smshenc@rdg.ac.uk) wrote:: I'd like to add to this discussion some references: concerning matrix derivaties. They are "Matrix : Derivatives" by Gerald Rogers and "Kronecker : Products and Matrix Calculus" with Applications by : A. Graham.

: BTW, Graham's book mentions that d|X|/dX is : |X|X^{-1}, which is just the adj(X), so the : question is how do you accurately compute the : adjugate of a matrix, right?

Usually given matrix formulae with inverses the best way tonumerically solve them is to rewrite as a system of equationsin LAPACK-et-al-compatible form without explicit inverses.

e.g. if the desired quantity Q is

Q = |X| X^{-1}

rewrite as

Q*X = |X|

and solve for Q with whatever library routine is appropriate. Oftenthey want the unknown multiplied on the right, so take transposes:

X^T * Q^T = |X|^T

{ A * UNKNOWN = B } (standard LAPACK template)

solve for Q^T, giving Q after post processing.

--Matthew B. Kennel/mbk@caffeine.engr.utk.edu/I do not speak for ORNL, DOE or UTOak Ridge National Laboratory/University of Tennessee, Knoxville, TN USA/